Ramsey-bordé ion frequency-reference apparatus, and methods of making and using the same

ABSTRACT

In some variations, an interferometric frequency-reference apparatus comprises: an atom source configured to supply neutral atoms; a collimator configured to form a collimated beam of the neutral atoms; one or more probe lasers; and a Doppler laser configured to determine a ground-state population of the neutral atoms. Other variations provide a method of creating a stable frequency reference, comprising: forming a collimated beam of neutral atoms; illuminating the neutral atoms with first and second probe lasers; adjusting the frequencies of the first probe laser and second probe laser using Ramsey spectroscopy to an S→D transition of the neutral atoms; and determining a ground-state population of the neutral atoms with another laser. The interferometric frequency-reference apparatus may provide an optical frequency reference or a microwave frequency reference.

PRIORITY DATA

This patent application is a continuation application of U.S. patentapplication Ser. No. 17/576,897, filed on Jan. 14, 2022, which claimspriority to U.S. Provisional patent application Ser. No. 63/159,167,filed on Mar. 10, 2021, each of which is hereby incorporated byreference herein.

FIELD OF THE INVENTION

The present invention generally relates to optical frequency references.

BACKGROUND OF THE INVENTION

Frequency standards are devices for producing or probing frequencies.Optical frequency standards refer to stable optical frequencies, and aregenerated by optical atomic clocks and optical cavities. Frequencystandards are useful in optical fiber communications, timing, radiofrequency (RF) photonics, and inertial sensing as well as othertechnologies. Application areas of ultraprecise optical frequencystandards include high-precision laser spectroscopy, miniature atomicinstruments (e.g. atomic clocks and gyroscopes), global positioningsystems, precision laser sensing (e.g., remote nuclear blast detection),and ultra-stable oscillators for high-speed analog-digital convertersand radar systems.

An active optical frequency standard is a laser source emitting lightwith a very well-defined and known optical frequency (e.g., stabilizedHeNe laser). A passive optical frequency standard is a passive devicewith a well-defined frequency response, which can be used to build anactive standard. Important examples are high-quality-factor referencecavities and devices such as multi-pass gas cells for probing certainoptical transitions.

An optical frequency standard is usually based on some optically probedelectronic transition (generally a dipole-forbidden butquadrupole-allowed transition) with a narrow frequency bandwidth ofatoms (e.g. Ca, Rb, Sr, Yb, Mg, or H), ions (e.g., Hg⁺, Sr⁺, Yb⁺, Ba⁺,In⁺, or Al⁺), or molecules (e.g., CH₄ or I₂). This electronic transitionis used to stabilize the frequency of a single-frequency laser to theelectronic transition frequency of the atom, ion, or molecule. In orderto reduce inhomogeneous broadening by thermal movement and collisions,the particles may be retained in a trap within a vacuum chamber alongwith laser cooling. This conventional set-up allows for precisespectroscopic measurements on the clock transition.

Papers describing frequency references include McFerran et al.,“Fractional frequency instability in the 10⁻¹⁴ range with a thermal beamoptical frequency reference”, J. Opt. Soc. Am. B, 27, 277-285 (2010);Norcia et al., “Frequency Measurements of Superradiance from theStrontium Clock Transition”, Phys. Rev. X 8, 021036 (2018);Davila-Rodriguez et al., “Compact, thermal-noise-limited referencecavity for ultra-low-noise microwave generation”, Opt. Lett. 42,1277-1280 (2017); Matei et al., “1.5 μm Lasers with Sub-10 mHzLinewidth”, Phys. Rev. Lett. 118, 263202 (2017); Kessler et al., “Asub-40-mHz-linewidth laser based on a silicon single-crystal opticalcavity”, Nature Photonics 6, 687-692 (2012); Cook et al.,“Laser-Frequency Stabilization Based on Steady-State Spectral-HoleBurning in Eu³⁺: Y₂SiO₅ ”, Phys. Rev. Lett. 114, 253902 (2015); andOlson et al., “Ramsey-Bordé Matter-Wave Interferometry for LaserFrequency Stabilization at 10⁻¹⁶ Frequency Instability and Below”, Phys.Rev. Lett. 123, 073202 (2019), each of which is hereby incorporated byreference.

Highly accurate optical frequency references play an important role inmany applications. Optical frequency references with better performancethan commercially available standards are desired, to enablehigh-precision spectroscopy at multiple locations, for example. Ingeneral, known frequency references are either extremely precise at thecost of massive size, weight, and power, or they sacrifice performancefor reduced size, weight, and power. Large optical cavity-basedfrequency references are currently the standard method of generating anoptical frequency reference at short integration/averaging times. Atlonger averaging times, optical atomic clocks are used.

There remains a long-felt need for a compact, ultra-stable, atom-basedfrequency reference that operates on short (e.g. <1 second) timescalesand demonstrates a high degree of stability on long time scales.

SUMMARY OF THE INVENTION

The present invention addresses the aforementioned needs in the art, aswill now be summarized and then further described in detail below.

In some variations, an interferometric frequency-reference apparatuscomprises:

-   -   a vacuum chamber;    -   an atom source configured to supply neutral atoms to be ionized;    -   an ionizer configured to excite the neutral atoms to form        ionized atoms (such as, but not limited to, Ca⁺ or Sr⁺);    -   an ion collimator configured to form a collimated beam of the        ionized atoms;    -   one or more probe lasers at a frequency near the clock        transition (e.g., quadrupole transition); and    -   a readout laser configured to determine a ground-state        population of the ionized atoms typically realized by measuring        a cycling transition of the atom such as the S-P transition in        Sr⁺,    -   wherein the atom source, the ionizer, and the ion collimator are        disposed within the vacuum chamber.

In some embodiments, the atom source is a solid-state electrochemicalatom source.

In some embodiments, the ionizer is disposed inside the ion collimator.In these embodiments, the ionized atoms are formed within the ioncollimator. In other embodiments, the ionizer is disposed outside theion collimator. In these embodiments, the ionized atoms are formed andthen injected into the ion collimator. The ionizer may be one or moreionizing lasers, electron-beam radiation, or similar.

In some embodiments, the ion collimator is a linear collimator. A linearcollimator may be selected from the group consisting of a linearquadrupole trap, a Penning trap, a surface ion trap, and a mass filter,for example. In other embodiments, the ion collimator is a non-linearcollimator. A non-linear collimator may be in a recirculatingconfiguration, such as a racetrack configuration, a ring, or a tortuousloop, for example.

The ion collimator may be configured such that the collimated beam ofthe ionized atoms has a beam waist selected from about 10 nanometers toabout 10 meters. Preferably, the beam waist is selected from about 50nanometers to about 500 nanometers. The ion collimator may be configuredsuch that the collimated beam of the ionized atoms has a beam velocityselected from about 1 μm/s to about 0.99 c, where c is the speed oflight in vacuum. Preferably, the beam velocity is selected from about 1m/s to about 20 m/s.

In some embodiments, one or more probe lasers are configured for Ramseyor Rabi spectroscopy on the ionized atoms. In preferred embodiments, allprobe lasers present are configured for Ramsey spectroscopy on theionized atoms. The number of probe lasers may vary but is preferably twoor more, such as four probe lasers (e.g., see FIG. 4 ).

In some embodiments, the one or more probe lasers are configured toprobe quadrupole or both dipole and quadrupole transitions of theionized atoms. Configuring includes selecting proper wavelength andensuring sufficiently narrow linewidth.

In some embodiments, the readout laser can be used for quantum jumpmeasurements. For quantum jump measurements, the readout laser may beused, post-Ramsey interrogation, via fluorescence from a S→P cyclingtransition.

In some embodiments, the interferometric frequency-reference apparatusfurther comprises a cooling laser. The cooling laser is configured tocool the ionized atoms in preparation for Ramsey spectroscopy. Incertain embodiments, the readout laser is itself configured for cooling,and there is not necessarily a physically distinct cooling laser.

The interferometric frequency-reference apparatus may further comprisean injection electrode. The injection electrode is different from theionizer. An injection electrode may create an electric potential fieldthat directs ionized atoms into the ion collimator, in embodimentswherein atoms are ionized outside the ion collimator. In preferredembodiments, atoms are ionized within the ion collimator; therefore, aninjection electrode is not necessary.

The interferometric frequency-reference apparatus may further comprisean ion sink configured to collect the ionized atoms exiting the ioncollimator. The ion sink is preferably disposed within the vacuumchamber.

The interferometric frequency-reference apparatus preferably furthercomprises an imaging system configured to focus fluorescence from theionized atoms.

The interferometric frequency-reference apparatus provides an opticalfrequency reference, in some embodiments. The interferometricfrequency-reference apparatus provides a microwave frequency reference,in some embodiments.

Other variations of the invention provide a method of creating a stablefrequency reference, the method comprising:

-   -   (a) creating an atomic vapor;    -   (b) ionizing at least some atoms in the atomic vapor, to form        ionized atoms;    -   (c) collimating the ionized atoms in an ion collimator, to form        a collimated beam of the ionized atoms;    -   (d) optionally, illuminating some of the ionized atoms with a        cooling laser;    -   (e) illuminating at least some of the ionized atoms with a first        probe laser at a first-probe-laser frequency;    -   (f) illuminating at least some of the ionized atoms with a        second probe laser at a second-probe-laser frequency;    -   (g) adjusting the first-probe-laser frequency and the        second-probe-laser frequency using Ramsey spectroscopy to an S→D        transition of at least some of the ionized atoms; and    -   (h) illuminating at least some of the ionized atoms with a        readout laser to determine a ground-state population of the        ionized atoms.

In some methods, the atomic vapor and/or the ionized atoms are obtainedfrom a solid-state electrochemical atom source. The ionized atoms may beCa⁺ and/or Sr⁺, in some embodiments.

The ionized atoms provided in step (b) may be formed within the ioncollimator provided in step (c). Alternatively, or additionally, theionized atoms provided in step (b) are formed and then injected into theion collimator. Steps (b) and (c) may be integrated such that at leastsome of the ionizing occurs inside ion collimator. In some preferredembodiments, steps (b) and (c) may be integrated such that all of theionizing occurs inside ion collimator.

In some methods, step (d) is conducted to cool the ionized atoms inpreparation for the Ramsey spectroscopy. The cooling may employ the samelaser as the readout laser (in which case it also is a cooling laser),or the cooling may employ a physically distinct laser.

In some methods, the ion collimator is a linear collimator. For example,the ion collimator may be a linear collimator selected from the groupconsisting of a linear quadrupole trap, a Penning trap, a surface iontrap, and a mass filter. In other methods, the ion collimator is anon-linear collimator. For example, the ion collimator may be anon-linear collimator selected from the group consisting of a racetrackconfiguration, a ring, a tortuous loop, or another recirculatingconfiguration.

The collimated beam of the ionized atoms may have a beam waist selectedfrom about 10 nanometers to about 10 meters, such as from about 50nanometers to about 500 nanometers. The collimated beam of the ionizedatoms may have a beam velocity selected from about 1 μm/s to about 0.99c, such as from about 1 m/s to about 20 m/s, where c is the speed oflight in vacuum.

In some embodiments, the method further comprises illuminating at leastsome of the ionized atoms with a third probe laser. In certainembodiments, the method further comprises illuminating at least some ofthe ionized atoms with a fourth probe laser after the illuminating atleast some of the ionized atoms with the third probe laser.

In preferred embodiments, the method is continuous, utilizing acontinuously moving atom beam (rather than stationary, trapped atoms)and a continuous-wave laser array with continuous interrogation.Reference to the atoms is continuously made as the atom beam passesthrough the cascade of laser beams, allowing direct fast-locking to theatomic transition. The use of an optical transition results in a higherresonance quality factor than RF transitions. The result of a continuousmethod is continuous fast readout of optical transitions, which is asignificant benefit for next-generation timing solutions.

In some methods, the stable frequency reference is an optical frequencyreference. In some methods, the stable frequency reference is amicrowave frequency reference.

Some methods utilize an interferometric frequency-reference apparatuscomprising: a vacuum chamber; an atom source configured to supplyneutral atoms to be ionized; an ionizer configured to excite the neutralatoms to form ionized atoms; an ion collimator configured to form acollimated beam of the ionized atoms; one or more probe lasers; and areadout laser configured to determine a ground-state population of theionized atoms, wherein the atom source, the ionizer, and the ioncollimator are disposed within the vacuum chamber.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a cross-section schematic of a linear quadrupole trapconfigured with rods.

FIG. 1B is a cross-section schematic of a linear quadrupole trapconfigured with blades.

FIG. 2 is a top view of a linear ion collimator, in some embodiments.

FIG. 3 is a top view of a non-linear ion collimator, in someembodiments.

FIG. 4 is a schematic of an interferometric frequency-referenceapparatus, in some variations.

FIG. 5 is a method flowchart, in some embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The apparatus, methods, and systems of the present invention will bedescribed in detail by reference to various non-limiting embodiments.

This description will enable one skilled in the art to make and use theinvention, and it describes several embodiments, adaptations,variations, alternatives, and uses of the invention. These and otherembodiments, features, and advantages of the present invention willbecome more apparent to those skilled in the art when taken withreference to the following detailed description of the invention inconjunction with the accompanying drawings.

As used in this specification and the appended claims, the singularforms “a,” “an,” and “the” include plural referents unless the contextclearly indicates otherwise. Unless defined otherwise, all technical andscientific terms used herein have the same meaning as is commonlyunderstood by one of ordinary skill in the art to which this inventionbelongs.

Unless otherwise indicated, all numbers expressing conditions,concentrations, dimensions, and so forth used in the specification andclaims are to be understood as being modified in all instances by theterm “about.” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in the following specification andattached claims are approximations that may vary depending at least upona specific analytical technique.

The term “comprising,” which is synonymous with “including,”“containing,” or “characterized by” is inclusive or open-ended and doesnot exclude additional, unrecited elements or method steps. “Comprising”is a term of art used in claim language which means that the named claimelements are essential, but other claim elements may be added and stillform a construct within the scope of the claim.

As used herein, the phrase “consisting of” excludes any element, step,or ingredient not specified in the claim. When the phrase “consists of”(or variations thereof) appears in a clause of the body of a claim,rather than immediately following the preamble, it limits only theelement set forth in that clause; other elements are not excluded fromthe claim as a whole. As used herein, the phrase “consisting essentiallyof” limits the scope of a claim to the specified elements or methodsteps, plus those that do not materially affect the basis and novelcharacteristic(s) of the claimed subject matter.

With respect to the terms “comprising,” “consisting of,” and “consistingessentially of,” where one of these three terms is used herein, thepresently disclosed and claimed subject matter may include the use ofeither of the other two terms. Thus in some embodiments not otherwiseexplicitly recited, any instance of “comprising” may be replaced by“consisting of” or, alternatively, by “consisting essentially of.”

In some variations, the present invention provides an ion-basedfrequency reference that provides an optical frequency standard withextremely high levels of stability and with fast, continuous readout, ina compact package. The invention is predicated, at least in part, on aRamsey-Bordé interferometer. A Ramsey-Bordé interferometer involves alinear stream of atoms probed by a well-defined sequence of oscillatoryfields. In the present invention, instead of using hot neutral atoms, acollimated stream of cooled, guided ions may be employed. The ions maybe guided by a specially designed radio-frequency (RF) Paul trap or amass filter designed precisely for this purpose. By employing a cooled,controlled stream of ions, a combination of features not available withany other frequency reference may be realized: (i) very low fractionalfrequency instability, (ii) fast, continuous readout, (iii) compact sizedue to reduced atom velocity, and/or (iv) reduced vacuum requirementsdue to deep trap depth.

To the knowledge of the present inventors, Ramsey-Bordé interferometryon a stream of cooled ions has not heretofore been accomplished. Asdescribed herein, Ramsey-Bordé interferometry on a stream of cooled ionsis performed with a high signal-to-noise ratio by utilizing an ioncollimator, such as an engineered RF-Paul trap/mass filter, thatcollimates the cooled ions and confines them to a one-dimensionalstream. In this disclosure, “trap/filter” is synonymous with “ioncollimator”. The trap/filter is configured to optimize the fractionalfrequency instability and the size, weight, and power of the device. Thetrap/filter controls the ion propagation velocity, thus significantlyreducing dimensional requirements, Doppler error, and transit timeerror. The trap/filter also provides a deep trapping potential to relaxvacuum requirements.

In this disclosure, “frequency reference” is synonymous with“interferometric frequency-reference apparatus” or like terms.

The stability and ultimate size of conventional Ramsey-Bordéinterferometers are limited by Doppler contributions to the error (firstand second order), and the transit-time broadening of the atomic speciesin relation to the laser beams. Historically, Ramsey-Bordé spectroscopyuses a beam of neutral atoms transiting an array of four lasers. Theneutral atom beam, used in the historical implementation, may bereplaced—according to this invention—with a collimated ion beam. Theapplied electric field of the trap/filter allows for precise velocitycontrol, as well as controlled density and spacing of the ions. Thisnovel use of an ion beam may significantly decrease Doppler broadeningand Ramsey-Bordé transit-time broadening suffered by the conventionalneutral-atom approach. Controlled ion-beam velocity also may enable longRamsey-Bordé transit times to be achieved without sacrificing size andpower requirements.

To date, atom-based frequency references (both RF and optical) employtrapped atoms whose transitions are probed via low-duty rate (on theorder of Hz), long-integration time spectroscopy. Reference to the atomscan necessarily be made only once per pulse sequence, resulting in atomfeedback that is very slow, on the order of seconds. By contrast, thepresent invention preferably utilizes a continuously moving atom beam(rather than stationary, trapped atoms) and a continuous-wave laserarray with continuous interrogation. Reference to the atoms iscontinuously made as the atom beam passes through the cascade of laserbeams, allowing direct fast-locking to the atomic transition. The use ofan optical transition results in a higher resonance quality factor thanRF transitions. The result of a continuous method is continuous fastreadout of optical transitions, which is a significant benefit fornext-generation timing solutions.

The frequency reference disclosed herein is enabled by the generation ofan ultranarrow-linewidth laser. The frequency reference can be used tolock a laser source for precision sensing/timing applications. Thefrequency reference can be used as an ultra-stable optical frequencyreference to which an external laser can be locked, via a standardbeat-note lock, for use by other optical, quantum, metrology, orcommunication instruments.

The present invention, in some variations, provides a fieldable (e.g.,on the order of 10 cm long) interferometric frequency-referenceapparatus with a stability competitive with conventional atomic clocks,operable at shorter averaging times, and with drift resistance greaterthan state-of-the-art cryogenic optical cavities.

While the disclosed device (interferometric frequency-referenceapparatus) may fill the niche of traditional stable oscillators, thedevice has other applications enabled by the realization of anultra-stable laser. One application is for precision sensing. An exampleof precision sensing is forensic seismology using undersea fiber-opticcables for standoff blast detection, where traditional seismometers areunavailable or impractical.

The present invention, in some variations, provides a compact frequencyreference with low fractional frequency instability (low Allandeviation) with fast continuous readout. Allan variance is the mostcommon statistical function used to characterize and classify frequencyfluctuations of a frequency reference. See Allan, Statistics of AtomicFrequency Standards, PROCEEDINGS OF THE IEEE Vol. 54, No. 2, 1966, whichis incorporated by reference. The Allan deviation (“ADEV”) is the squareroot of the Allan variance. ADEV is used to characterize the randomdeviations which are related to the noise in the frequency. While thereare other ways to define fractional frequency instability includingmodified Allan deviation, in this disclosure, “fractional frequencyinstability” means the unitless Allan deviation, ADEV, defined above.

The present invention, in various embodiments, provides multiplebenefits over prior and state-of-art optical frequency references. Thefrequency reference is fundamentally limited only by atomic propertiesand therefore is capable of long-term averaging, unlike cavities aspassive optical resonators. The limit of fractional frequency stabilityis therefore the fundamental stability limit of about 10⁻¹⁸ (ADEV),dictated by quantum physics.

The frequency reference disclosed herein does not require cryogenicoperation or any cryogenic components.

Unlike conventional optical clocks, the frequency reference has fastreadout without the need for systematic calibration.

With cooled atoms, the propagation length of the atomic beam can beproportionally reduced as the beam size is set by the velocity of theatoms relative to the intrinsic atomic quadrupole linewidth.

By using trapped ions instead of neutral atoms, a higher degree ofcontrol may be realized for the atomic velocity distribution. Exemplaryion-trap/filter geometries include a linear filter and a racetrack trapgeometry. A linear filter is conceptually simpler, while a racetracktrap geometry enables cancelling residual Doppler broadening, and may beuseful to turn off the atomic sources for recycling the ions.

The conventional frequency references with the lowest fractionalfrequency instability to date are optical atomic clocks. They hold theworld record in fractional frequency instability which is on the orderof 10⁻¹⁸. However, the extreme complexity and massive size/weight/powerrequirements disqualify optical atomic clocks for practical deployment.Furthermore, optical atomic clocks require their lasers to be locked tolarge (˜40 cm long) or cryogenic optical cavities. The laser lockingnarrows the laser linewidth and provides an electromagnetic source (thelaser) as a stable optical oscillator. However, the optical cavities arelarge, operate at their fundamental limits, and do not achieve long-termstability sufficient to enable standalone operation without an opticalatomic clock. There have been a few demonstrations of atomic-basedfrequency references but they are physically large because their size isset by the atomic velocity distribution and/or cryogenic operation. Anyattempt to miniaturize lab-scale optical atomic clocks must solve therequirement of optical frequency references in order to operate.

Most fieldable frequency references are high-quality-factorradio-frequency cavities—e.g., oven-controlled crystal oscillators(OCXOs)—which are interfaced with standard electronics. While appealingin terms of size/weight/power requirements, such frequency referencesare based on a material like quartz that experiences long-term driftsand cannot be used in situations where long-term stability is required(ADEV≈10⁻¹⁰-10⁻¹³)

For applications requiring timing and long-term stability superior toOCXOs while maintaining deployability (e.g., Global Positioning Systemapplications), warm radio-frequency atomic clocks are used. However,these clocks are still complex, requiring their own separate precisionoscillator just to read them out which is limited to very longtime-scales. Subsequently, chip-scale atomic clocks are almost alwayspaired with their own highly stable frequency reference. Yet, theirperformance is still on the order of ADEV 10⁻¹³ on short time scales,and only improving on long time-scales such as greater than 100 seconds.

In preferred embodiments, a significant difference between the disclosedfrequency reference compared to state-of-art Ramsey-Bordéinterferometers or atomic clocks is that the hot neutral atoms in aninterferometer, or cold trapped atoms in a clock, are replaced with acontinuously moving ion beam.

Another significant difference with conventional art is that, inpreferred embodiments, the disclosed frequency reference replaces pulsedlasers (in a clock) with a sequence of spatially separatedcontinuous-wave lasers. By implementing a Ramsey-Bordé interferometer ina guided-ion (collimated) system, a continuous beam of atoms is used forfast readout while avoiding the velocity distribution problems ofneutral atoms.

Another difference with conventional art is that the disclosed frequencyreference, in preferred embodiments, greatly relaxes the requirementsfor complex cooling procedures. Preferred frequency references employminimal laser cooling and then trapping/guiding ions in a deepradio-frequency (RF) potential field. Deeper traps can be made with theRF-Paul trap than with typical magnetic-field traps needed for neutralatoms. Further, deep RF-Paul traps allow for control of propagationvelocity. Preferred methods exclusively utilize radio-frequency anddirect-current fields, thereby requiring fewer lasers. The disclosedfrequency reference is compatible with solid-state paths to integration,and is more amenable to miniaturization.

In some variations, an interferometric frequency-reference apparatuscomprises:

-   -   a vacuum chamber;    -   an atom source configured to supply neutral atoms to be ionized;    -   an ionizer configured to excite the neutral atoms to form        ionized atoms (such as, but not limited to, Ca⁺ or Sr⁺;    -   an ion collimator configured to form a collimated beam of the        ionized atoms;    -   one or more probe lasers; and    -   a readout laser configured to determine a ground-state        population of the ionized atoms,    -   wherein the atom source, the ionizer, and the ion collimator are        disposed within the vacuum chamber.

In some embodiments, the atom source is a solid-state electrochemicalatom source. Integration with a solid-state electrochemical atomic beamsource can reduce size, weight, and power as the frequency reference issmaller, is more power-efficient, and provides a collimated beam whencompared to conventional atomic ovens.

In some embodiments, the ionizer is disposed inside the ion collimator.In these embodiments, the ionized atoms are formed within the ioncollimator. In other embodiments, the ionizer is disposed outside theion collimator. In these embodiments, the ionized atoms are formed andthen injected into the ion collimator.

In some embodiments, the ion collimator is a linear collimator. A linearcollimator may be selected from the group consisting of a linearquadrupole trap, a Penning trap, a surface ion trap, and a mass filter,for example. FIG. 1A is a cross-section schematic of a linear quadrupoletrap configured with rods. FIG. 1B is a cross-section schematic of alinear quadrupole trap configured with blades. FIG. 2 is a top view of alinear ion collimator, in some embodiments.

In other embodiments, the ion collimator is a non-linear collimator. Anon-linear collimator may be in a recirculating configuration, such as aracetrack configuration (e.g., see FIG. 3 ), a ring, or a tortuous loop,for example. FIG. 3 is a top view of a non-linear ion collimator, insome embodiments.

The ion collimator may be configured such that the collimated beam ofthe ionized atoms has a beam waist selected from about 10 nanometers toabout 10 meters. Preferably, the beam waist is selected from about 50nanometers to about 500 nanometers. The ion collimator may be configuredsuch that the collimated beam of the ionized atoms has a beam velocityselected from about 1 μm/s to about 0.99 c, where c is the speed oflight in vacuum. Preferably, the beam velocity is selected from about 1m/s to about 20 m/s.

In some embodiments, one or more probe lasers are configured for Ramseyspectroscopy on the ionized atoms. In preferred embodiments, all probelasers present are configured for Ramsey spectroscopy on the ionizedatoms. The number of probe lasers may vary but is preferably two ormore, such as four probe lasers (e.g., see FIG. 4 ).

In some embodiments, the one or more probe lasers are configured toprobe quadrupole or both dipole and quadrupole transitions of theionized atoms. Configuring includes selecting proper wavelength andensuring sufficiently narrow linewidth.

In some embodiments, the readout laser is a Doppler laser configured toperform a quantum-jump measurement to determine the ground statepopulation, post-Ramsey interrogation, via fluorescence from a S→Pcycling transition.

In some embodiments, the interferometric frequency-reference apparatusfurther comprises a cooling laser. The cooling laser is configured tocool the ionized atoms in preparation for Ramsey spectroscopy. Incertain embodiments, the readout laser is itself configured for cooling,and there is not necessarily a physically distinct cooling laser.

The interferometric frequency-reference apparatus may further comprisean injection electrode. The injection electrode is different from theionizer. An injection electrode may create an electric potential fieldthat directs ionized atoms into the ion collimator, in embodimentswherein atoms are ionized outside the ion collimator. In preferredembodiments, atoms are ionized within the ion collimator; therefore, aninjection electrode is not necessary.

The interferometric frequency-reference apparatus may further comprisean ion sink configured to collect the ionized atoms exiting the ioncollimator. The ion sink, if present, is preferably disposed within thevacuum chamber.

The interferometric frequency-reference apparatus preferably furthercomprises an imaging system configured to focus fluorescence from theionized atoms. The imaging system may include an optical lens or systemof lenses, a camera, a photomultiplier tube, and/or a photon bucketdetector.

FIG. 4 is a schematic of the interferometric frequency-referenceapparatus, in some variations. The frequency reference shown in FIG. 4includes a vacuum chamber, an atom source, an ionizer, an ioncollimator, an injection electrode, an ion sink, four probe lasers, aDoppler laser (generally, a readout laser), and an imaging system. Theinjection electrode and the imaging system are optional components.

In certain embodiments, an interferometric frequency-reference precursorapparatus is provided without the vacuum chamber. At a later time, theprecursor apparatus is situated within a vacuum chamber. Theinterferometric frequency-reference precursor apparatus, prior todisposition within a vacuum chamber, comprises:

-   -   an atom source configured to supply neutral atoms to be ionized;    -   an ionizer configured to excite the neutral atoms to form        ionized atoms (such as, but not limited to, Ca⁺ or Sr⁺);    -   an ion collimator configured to form a collimated beam of the        ionized atoms; one or more probe lasers; and    -   a readout laser configured to determine a ground-state        population of the ionized atoms.

The interferometric frequency-reference apparatus provides an opticalfrequency reference, in some embodiments. The interferometricfrequency-reference apparatus provides a microwave frequency reference,in some embodiments.

Other variations of the invention provide a method of creating a stablefrequency reference, the method comprising:

-   -   (a) creating an atomic vapor;    -   (b) ionizing at least some atoms in the atomic vapor, to form        ionized atoms;    -   (c) collimating the ionized atoms in an ion collimator, to form        a collimated beam of the ionized atoms;    -   (d) optionally, illuminating some of the ionized atoms with a        cooling laser;    -   (e) illuminating at least some of the ionized atoms with a first        probe laser at a first-probe-laser frequency;    -   (f) illuminating at least some of the ionized atoms with a        second probe laser at a second-probe-laser frequency;    -   (g) adjusting the first-probe-laser frequency and the        second-probe-laser frequency using Ramsey spectroscopy to an S→D        transition of at least some of the ionized atoms; and    -   (h) illuminating at least some of the ionized atoms with a        readout laser to determine a ground-state population of the        ionized atoms.

FIG. 5 depicts a method flowchart, in some embodiments. The steps ofilluminating ions with a cooling laser, illuminating ions with a thirdprobe laser, and illuminating ions with a fourth probe laser, areoptional. The readout laser may be a Doppler laser. The step ofilluminating ions with a Doppler laser (or other readout laser) may beperformed before or after the step of adjusting the frequency of theprobe lasers using Ramsey spectroscopy.

In some methods, the atomic vapor and/or the ionized atoms are obtainedfrom a solid-state electrochemical atom source. The ionized atoms may beCa⁺ and/or Sr⁺, in some embodiments. Solid-state electrochemical atomsources are described in more detail later in this detailed description.

The ionized atoms provided in step (b) may be formed within the ioncollimator provided in step (c). Alternatively, or additionally, theionized atoms provided in step (b) are formed and then injected into theion collimator. Steps (b) and (c) may be integrated such that at leastsome of the ionizing occurs inside ion collimator. In some preferredembodiments, steps (b) and (c) may be integrated such that all of theionizing occurs inside ion collimator.

In some methods, step (d) is conducted to cool the ionized atoms inpreparation for the Ramsey spectroscopy. The cooling may employ the samelaser as the readout laser (in which case it also is a cooling laser),or the cooling may employ a physically distinct laser.

In some methods, the ion collimator is a linear collimator. For example,the ion collimator may be a linear collimator selected from the groupconsisting of a linear quadrupole trap, a Penning trap, a surface iontrap, and a mass filter. In other methods, the ion collimator is anon-linear collimator. For example, the ion collimator may be anon-linear collimator selected from the group consisting of a racetrackconfiguration, a ring, a tortuous loop, or another recirculatingconfiguration.

The collimated beam of the ionized atoms may have a beam waist selectedfrom about 10 nanometers to about 10 meters, such as from about 50nanometers to about 500 nanometers. The collimated beam of the ionizedatoms may have a beam velocity selected from about 1 μm/s to about 0.99c, such as from about 1 m/s to about 20 m/s, where c is the speed oflight in vacuum.

In some embodiments, the method further comprises illuminating at leastsome of the ionized atoms with a third probe laser. In certainembodiments, the method further comprises illuminating at least some ofthe ionized atoms with a fourth probe laser after the illuminating atleast some of the ionized atoms with the third probe laser.

In some methods, the stable frequency reference is an optical frequencyreference. In some methods, the stable frequency reference is amicrowave frequency reference.

Some methods utilize an interferometric frequency-reference apparatuscomprising: a vacuum chamber; an atom source configured to supplyneutral atoms to be ionized; an ionizer configured to excite the neutralatoms to form ionized atoms; an ion collimator configured to form acollimated beam of the ionized atoms; one or more probe lasers; and areadout laser configured to determine a ground-state population of theionized atoms, wherein the atom source, the ionizer, and the ioncollimator are disposed within the vacuum chamber.

Some variations will now be further described in greater detail, itbeing understood that such description is non-limiting and that thepresent invention is not limited by any hypotheses or theories.

The interferometric frequency-reference apparatus is a device thatRamsey-interrogates a collimated ion beam to directly fast-feedback-lockan ultra-stable laser. Reference is made to FIG. 4 showing componentsand optional components.

The vacuum chamber houses the atom source, the ion sink, the ionizer,and an ion collimator such as a modified RF ion Paul filter/trap. Sincethe ions are collimated, and not trapped per se, the requirements forultra-high vacuum (to reduce background collisions) are relaxed comparedto conventional ion trapping. The vacuum level may be moderate, such asa chamber pressure in the range of about 10⁻⁵ torr to about 10⁻⁸ torr.The laser array and the imaging system may be placed inside or outsidethe vacuum chamber, depending on whether these components are compact.The vacuum chamber may be a standard off-the-shelf (e.g. stainlesssteel) chamber or may be a custom-built vacuum chamber from stainlesssteel, aluminum, borosilicate glass, aluminosilicate glass, sapphire, ora combination thereof, for example.

The atom source supplies a stream of neutral atoms to be ionized. Thestream of neutral atoms is in a vapor phase containing the atoms. Theatom source may be positioned at or near the entrance of the ioncollimator. The atom source may be a separate chamber with a conductancerestriction with its aperture near the ionizer, a SAES dispenser, a pilldispenser, an alfasource dispenser, a liquid or solid phase of the atoms(possibly mixed with other species), a LIAD (light induced atomicdesorption) source, a graphite (or other) intercalation compound of theatoms, or an electrochemical solid-state source, for example. See thesection entitled Solid-State Electrochemical Atom Sources later in thisspecification, regarding embodiments of electrochemical solid-state atomsources that may be utilized in the frequency reference herein. Theneutral atoms to be ionized may be selected from the group consisting ofCa, Sr, Yb, Li, Na, K, Rb, Cs, Hg, and combinations thereof, forexample. In some embodiments, the atoms are Ca and/or Sr, assingle-electron ionization of calcium or strontium results in hydrogenicions with a broad cycling dipole transition and a narrow quadrupoletransition, both easily addressable by commercial lasers. The atomicspecies may be isotopically enriched relative to its natural isotopicabundance.

The ionizer excites the neutral atoms, promoting a valence electron fromthe atom to the continuum and leaving behind an ion, such as ahydrogenic ion. The ionizer may employ photoionization, i.e. ionizationproduced by the action of electromagnetic radiation (e.g., opticalradiation). Some embodiments employ two-photon optical ionization, inwhich an ECDL (external cavity diode laser) is tuned to the neutralatoms' electric dipole transition (S→P), exciting a valence electronfrom the ground S state to an excited P state. From there, a second ECDLpromotes the P-state electron to the continuum. Both laser beams arepreferably focused near the entrance of the ion collimator. Opticalionization allows isotope selection: the first ECDL may befrequency-tuned to selectively ionize one out of multiple naturallyoccurring isotopes in the atomic sample (typical isotope shifts arelarge, on the order of GHz—easily addressable by a MHz-broad laser).Frequency tuning may be accomplished by a loose, easily engineered DAVLL(dichroic atomic vapor laser lock) lock to a vapor cell filled with theneutral atoms. The second ECDL need not be frequency-stabilized at all.The disadvantage of this method is the need for a dedicated ionizinglaser (the first S→P laser). The second, P→continuum laser maysimultaneously be used as a readout laser.

Alternatively, or additionally, the ionizer may employ electricalionization. With electrical ionization, a small current-carryingfilament may be placed near the neutral atom beam leaving the atomsource, to excite a valence electron directly into the continuum. Whilethis technique obviates the need for a dedicated ionizing laser, thereis not selectivity for certain isotopes. Thus, an isotopically enrichedatom source would be required, if it is desired for the frequencyreference to utilize isotopically enriched atoms. Electrical ionizationtends to be the preferred ionization technique when prioritizing size,weight, and power requirements.

The ion collimator (trap) is used to collimate the ionized atoms into aone-dimensional, velocity-controlled beam. The collimated beam travelsalong the length of the trap, through a sequence of spatially separatedlasers for cooling, Ramsey interrogation, and readout. The ioncollimator may be a modified RF ion mass filter. In some embodiments,the ion collimator contains the ionizer within the ion collimator. Inother embodiments, the ion collimator receives ions separately generatedby an ionizer that is physically disposed outside the ion collimator.

Many geometries of ion collimators may be used. A linear collimator maybe a modified RF ion mass filter, with four parallel (e.g. tungsten)rods (FIG. 1A) or blades (FIG. 1B). Two of the rods/blades support MHzRF, such as supplied by an amplified RF function generator, while theother two rods/blades are held at direct current (DC), tied to adigital-to-analog converter. This standard configuration provideslongitudinal trapping (x, y), ensuring that the ion beam remainscollimated into a one-dimensional crystal axially (z). The DC rods maybe segmented (with different DC voltages) to provide transport controlof the ion beam axially. In this way, the ion beam may be continuouslytransported along the collimator with a well-controlled velocitydistribution. This velocity control is very beneficial when thefrequency reference is an ultra-narrow frequency reference.

Unlike a conventional RF ion trap, the linear collimator preferably doesnot include DC endcaps that would cause harmonic axial trapping.Instead, the ion collimator produces a slow-moving ion beam, which isnot trapped in all three dimensions. The linear design of the ioncollimator may be similar to ion-based mass filters, which normallyoperate in high vacuum ranges. However, because long trap lifetimes arenot required, the vacuum level may be relaxed compared to typical iontraps.

The rods/blades of the ion collimator may be machined and aligned in a(e.g. Macor) support structure, such as a structure fabricated fromMacor® machinable glass ceramic (Corning Incorporated, Corning, N.Y.,USA). The rods/blades may be fabricated from metal deposited in stripsonto the walls of a hollowed-out, machined (e.g. laser-machined) part,such as a piece of fused silica. Typical sizes are about 30 cm×10 cm×10cm for a Macor structure, and about 10 cm×3 cm×1 mm for a laser-machinedsystem. If stability and simplicity is a priority, then the smallerlaser-machined design is preferred.

The ion collimator may be a non-linear collimator, such as a racetrackcollimator. A racetrack collimator (see FIG. 3 ) essentially bends thelinear collimator and connects the ends together to form a racetrackshape. In this configuration, residual Doppler shifts may be cancelledby interrogating two opposite-momentum ion beams. A racetrackcollimator, or other recirculating configuration, may utilize acommercial ion pump to maintain vacuum. Ion collimators withrecirculating configurations provide long atom-source lifetimes.

Ions leaving the ion collimator may be collected by an ion sink forrecycling. The ion sink is an optional component which may be especiallybeneficial in the case of a linear collimator. The ion sink may bepositioned on the output port of the ion collimator to collect the ionbeam after use. The ion sink may be an electrochemical solid-state atomsink, which may be similar to an electrochemical solid-state atom sourcebut designed to act as an atom sink. In certain embodiments, the atomsource is repurposed as an ion sink, which may significantly increasethe lifetime of the device. For example, upon depletion of the atomsource, the ion sink may be repurposed as the new source, directing anatom beam in the opposite direction along the ion collimator. The ionbeam may then be collected by the original atom source (now itselfrepurposed as an ion sink).

Other implementations of an atom sink include, but are not limited to, agraphite intercalation compound, a mixture of the atomic species withalkali or alkaline earth metals, or a cold surface. The atom sink, onceit contains a high amount of absorbed, adsorbed, or intercalated atoms,may then be heated to release the atomic species of interest. Theinitial atom source may be cooled to turn it into an atom sink, therebyreversing the flow of atoms and ions, permitting reuse of atoms, andenabling a longer device lifetime and/or a smaller atom source size.

A laser array includes an optional cooling laser, one or more probelasers, and a Doppler laser functioning as a readout laser. The laserarray is preferably arranged orthogonally to the propagation directionof the ions. The laser array is configured to perform a Ramseyinterrogation sequence on the ion beam as the ions move through the ioncollimator.

A Doppler laser, or other cooling laser, may be used to initialize theion beam into the S state in preparation for Ramsey interrogation.Slightly red-detuned with respect to a S→P electric dipole transition ofthe ion (a broad cycling transition with high scattering rate), theDoppler laser cools the ion beam to the Doppler limit (e.g., atemperature of about 70 mK) and into the Lamb-Dicke regime wherefirst-order Doppler shifts are separable into motional sidebands. Thelaser may be a small external-cavity diode laser (ECDL) of intermediatepower (a few mW), locked to prevent accidental blue-detuned heating ofthe ions. A small commercial cavity, with a Pound-Drever-Hall (PDH)lock, may be used for this purpose. Depending on the atom specieschosen, one or more red-wavelength repump lasers may also be utilized tokeep the ion in the Doppler cooling cycle. Such repump lasers have evenless stringent power and locking requirements; an inexpensivedistributed feedback (DFB) laser may be used, locked only to a slowwavemeter.

A probe laser is locked to a narrow transition in the ion via opticalRamsey spectroscopy. In the case of Ca⁺ or Sr⁺, the narrow transition isa ˜Hz-wide electric quadrupole S→D transition. Quadruple transitions areclock transitions, do not emit light very well, have long coherence, andhave high quality factor (Q). In order to perform spectroscopy withenough precision to resolve the Ramsey fringe pattern, the laser ispreferably pre-stabilized, narrowed to ˜kHz laser linewidth via a PDHlock to an ultralow-expansion (ULE) cavity. Note that this cavity neednot be narrowed to laser linewidths of mHz. To sweep the laserfrequency, a small amount of tuning (100s of kHz) is enabled bydirecting the probe laser beam, post-lock, through an acoustic-opticalmodulator (AOM).

Table 1 below lists laser wavelengths for cooling/detection, quadrupoletransition, and repumping for Sr⁺ and Ca⁺ ions, in exemplaryembodiments.

TABLE 1 Laser Wavelengths for Strontium and Calcium Ions Used in anInterferometric Frequency-Reference Apparatus. Sr⁺ Ca⁺ Cooling/Detection421.7 nm 396.8 nm Repump 1 1091.5 nm 866.2 nm Repump 2 1033 nm 729 nmQuadrupole 674 nm 854 nm

Both a Ramsey and a Ramsey-Bordé spectroscopy sequence are available foroperation of the device. The Ramsey sequence may be understood asconsisting of only the first two pulses from a Ramsey-Bordé pulsesequence. A Ramsey-Bordé spectroscopy sequence is now detailed, as it isseen by the ions in their own reference frame as they pass throughcontinuous-wave laser array. In the ions' frame of reference, thesequence consists of four coherent π/2 pulses, all preferably at thesame frequency.

(1) The first π/2 pulse promotes the ion from the S state to a coherentsuperposition of S and D states. After the π/2 pulse, the ion evolvesfreely for some time τ, which may be referred to as the Ramseyinterrogation time. If measured in a rotating frame during this time, aphase delay between the local oscillator (the probe laser) and therotation of the state vector in the Bloch sphere will develop, if andonly if the probe laser is detuned from the atomic transition.

(2) The second π/2 pulse is pulsed at the end of the Ramseyinterrogation time τ. Depending on the phase delay acquired during theinterrogation time, the ion will return to the ground state S withwell-defined probability or will be excited to the D state.

(3) The third π/2 pulse is a counter-propagating pulse that excites theion after the first Ramsey interrogation time with a small delay T. Thisπ/2 pulse causes the atom to again become a coherent superposition of Sand D states during time t. However, it now acquires a phase that isnegative with respect to the first interrogation time T. This stimulatesecho, effectively canceling low-frequency dephasing from unwanted noisesources. It is a well-known technique, often called a stimulated photonecho, which is an optical analog of a stimulated spin echo. Preferable,it is ensured that τ=t for all measurements.

Preferably, the first, second, and third π/2 pulses remain maximallyphase-coherent. Otherwise, phase jitter of the probe laser with respectto the ion beam—due to acoustic vibration physically moving the laseroutput and possibly causing Doppler shifts—can significantly diminishRamsey fringe contrast. As such, in preferred embodiments, the phasestability of the laser beam path is actively stabilized via a smallMach-Zehnder (MZ) beam-splitter interferometer.

(4) A fourth and final π/2 pulse converts the ion into either an S or Dstate. The probability of becoming excited (D state) or unexcited (Sstate) is determined by the phase acquired during the Ramseyinterrogation (τ, t) times. As a population state, readout is determinedby measuring fluorescence realized by the cycling/Doppler laser. Sincethe probability of being in the S or D state is in part a function ofthe probe laser's detuning from the atomic transition, sweeping theprobe laser frequency via the post-lock AOM discussed above leads to theappearance of Ramsey fringes, to which the probe laser can be locked(locking electronics are discussed below).

In some embodiments, the velocity distribution of the ion beam isdelta-function-like to ensure constant Ramsey interrogation time τ, fromion to ion, thereby minimizing loss of Ramsey fringe contrast. Also notethat the fringe features have a width 1/τ, so τ is preferably as long aspossible, limited by decoherence times and readout speed and lockbandwidth. The velocity control of the ion beam provided by the ioncollimator is a substantial benefit.

A readout laser is employed to perform a quantum jump measurement inorder to determine the ground state population, post-Ramseyinterrogation. The readout laser may be the same Doppler laser that wasused for cooling, via a beam split, or may be a different Doppler laser.The quantum-jump measurement utilizes fluorescence from the S→P cyclingtransition. If the measurement collapses the ion's wavefunction into theS ground state, then the ion will cycle on the S→P transition and willfluoresce. Otherwise, if the wave function collapses to the excited Dstate, then the ion will be outside the cycling transition and in a darkstate. Repeated fluorescence measurements, using an imaging system,quickly gives a measure of the probability of a successful quantum jump.

The imaging system comprises a photomultiplier tube (PMT) and a lens tofocus ion fluorescence onto the PMT aperture. Readout can either betaken as an average of ions as they pass by, or single-shot (ion-by-ion)with a field-programmable gate array to gate photon arrivals with ionsas they pass. Ultimately, ion velocity and spacing will set the readouttime, along with the cycling transition's scattering rate. The estimatedreadout time can be realized from the following equations. Consider thetime for an ion to transit an ion mass filter. This is given byT_(a1)=d_(RB)/V_(atoms) where d_(RB) is the trap length and V_(atoms) isthe velocity of the ion beam. Subsequently, a second ion immediatelyfollowing the first must be read out at a timeT_(a2)=d_(RB)/V_(atoms)+d_(atom)/V_(atoms) where d_(atom) is theatom-atom spacing. Thus, the measurement update time is set byT_(m)=d_(atom)/V_(atoms), i.e. it is the time between successive ion-ionmeasurements. An upper bound for the measurement time/bandwidth can befound by considering a 7.62-cm-long ion trap and a velocity of 76m/s—this corresponds to T_(m)=65 nanoseconds, a rate of about 15 MHz(1/T_(m)). This would be the fastest rate at which the laser linewidthcan be updated for readout. Note for Ca⁺ and Sr⁺, the cycling transitionlinewidth is about 20 MHz. Ultimately there is no benefit by having afaster ion-ion update rate beyond about 20 MHz, since the fastest asingle ion can be read out is fundamentally set by this rate.

The interferometric frequency-reference apparatus is preferablyconfigured with locking electronics for frequency locking, utilizingPID—Proportional (P), Integral (I), and Derivative (D) feedback control.A conventional operational amplifier, with feedback loop, may be used tokeep the probe laser frequency-locked to a side of Ramsey fringe. Ramseyfringe width is set by 1/τ, and the narrower the fringe the tighter thelock (and thus the narrower the locked laser). However, the fringe mustnot be so narrow as to have a narrow lock range that can easily beunlocked. An input to the feedback loop may be the error, calculated asreading minus setpoint, where reading is the measured, calibratedquantum jump probability determined by the readout laser, and setpointis determined in-circuit. An output to the feedback loop may beP×error+I, where I is the integral of error as a function of time. Thefeedback is conveyed to the acousto-optic modulator described above. Insome embodiments, the feedback is also conveyed partially to the probelaser, depending on the type of laser.

The interferometric frequency-reference apparatus may include a residualamplitude modulation feedback system. The interferometricfrequency-reference apparatus may be configured to stabilize or polarizeinput light to an electro-optic modulator (EOM).

The interferometric frequency-reference apparatus has primarily beendescribed as a standalone optical frequency reference. If desiredoperation is for an ultra-stable microwave frequency source, then ahigh-repetition-rate frequency comb (e.g., 10 GHz) is preferably lockedto the ultra-stable narrow linewidth laser using a similar PID lock asdisclosed above. The locking of a comb-line to the ultra-narrowlinewidth transfers the stability of the narrow-linewidth laser to thefrequency comb. In a fully self-referenced system, the rate at which thefrequency comb's ˜200 femtosecond pulses come out of the laser (a rateof about 10 GHz) becomes locked with the stability of the opticalreference. The detection of these pulses on a photodiode creates anultra-stable microwave frequency reference. Frequency combs may bepurchased commercially for this purpose. Alternatively, two or moredevices (as disclosed herein) may be used to perform frequency transfer.In some embodiments, a microwave frequency reference is generated bybeating two independent devices against each other. The resulting beatnote may have the relative stability of an optical frequency reference.

This invention is applicable to portable atomic instruments, sensors,and lasers. Current electronic-warfare systems would benefit from highlystable local oscillators which would enable analog-digital converters tooperate at higher frequency and with more bits. Similarly, radar systemsbenefit from lower local oscillator noise enabling the detection ofslow-moving objects and for SAR at higher or geosynchronous orbit.Additionally, there is a need for ultra-narrow lasers for standoffforensic seismology (blast detection) using underwater fiber opticcables.

The interferometric frequency-reference apparatus may be fabricated in awide range of sizes, such as from about 1 cm³ to about 100 cm³ in totaldevice volume, for example. In some embodiments, the size of theinterferometric frequency-reference apparatus is less than 100 cm³, lessthan 10 cm³, or less than 1 cm³.

The interferometric frequency-reference apparatus may be operatedaccording to the following examples, which are by no means limiting.

In one example, the interferometric frequency-reference apparatus, withits output, is treated as a “black box” functioning as an ultra-stablelaser. Ultra-stable lasers have a variety of applications in timing,sensing, and spectroscopy.

In another example, the interferometric frequency-reference apparatus isutilized for generating RF timing. Two or more of the devices may beused for RF clock generation by beating the output lasers against eachother. The beat note will then contain the relative stability of the twodevices, down-converted to a radio frequency.

Another method for generating an RF clock may be realized by locking anoptical frequency comb to the ultra-stable laser. In this scenario, therepetition rate of the frequency comb serves as the RF clock with thestability of the ultra-stable laser transferred to the stability of thecomb repetition rate.

The interferometric frequency-reference apparatus may be utilized as astable clock. On a satellite, submarine, or other vehicle, a stableclock allows long times (years) for secure communication even in aGPS-denied environment. This contrasts with the existing state-of-artsecure communication, which is only on a time scale of minutes.

For space-based radar, the disclosed interferometric frequency-referenceapparatus—working as a stable clock—enables (i) the identification ofslow-moving targets, (ii) the removal of clutter from radar returnsignals, (iii) the ability to have geosynchronous synthetic apertureradar (SAR) with millimeter resolution, and (iv) longer integrationtimes for SAR satellites.

The disclosed interferometric frequency-reference apparatus may be anultra-stable laser in optical atomic clocks. In optical atomic clocks,an ultra-stable laser is a critical component to optical atomic clockminiaturization. An ultra-stable laser acts to replace the cryogeniccavities used to generate stable lasers in state-of-art optical clocks.

The disclosed interferometric frequency-reference apparatus may be anultra-stable laser in spectroscopy. In spectroscopy, an ultra-stablelaser provides a tool to study vary narrow radioactive elements (nucleartransitions) by transferring its stability to another laser. As such,the device disclosed herein may be useful for nuclear state-of-matterexperiments. Also, in spectroscopy, an ultra-stable laser locked to anatomic reference can act as an absolute frequency calibration sourcerelevant for future astronomy experiments.

Solid-State Electrochemical Atom Sources

Some variations utilize an atomic-beam source device as a solid-stateelectrochemical atom source, wherein the atomic-beam source devicecomprises:

-   -   a first electrode;    -   a second electrode that is electrically isolated from the first        electrode; and    -   a first ion conductor interposed between the first electrode and        the second electrode, wherein the first ion conductor is capable        of transporting metal ions, and wherein the first ion conductor        is in contact with the first electrode and with the second        electrode.

The atoms that are emitted (as atomic vapor) from the atomic-beam sourcedevice may be alkali metal atoms, alkaline earth metal atoms, rare earthmetal atoms, mercury, or a combination thereof. For example, the metalatoms may be selected from the group consisting of Rb, Cs, Ca, Na, K,Sr, Li, Yb, Hg, and combinations thereof. Other metal atoms may beemitted from the atomic-beam source device, including Si, Ga, Al, In,As, Sb, Ge, Sn, Pb, Mg, Ba, Te, Au, Pt, Cr, and Cd, for example.

A voltage may be applied for a given duration across two electrodes thatare situated on opposite sides of the first ion conductor, to sourceatoms. The voltage polarity may be switched so that the atomic-beamsource device becomes an atom sink. The voltage amplitude is selected tocontrol the atom flux.

In various embodiments, the applied voltage between two electrodes isfrom about 0.01 V to about 100 V, such as from about 0.1 V to about 10V. The device power input for sourcing metal atoms is preferably lessthan about 500 mW, more preferably less than about 200 mW, and mostpreferably less than about 100 mW.

An “electrode” is a region that is electrically conductive or includesone or more material phases that are themselves electrically conductive.The first electrode permits the conduction of electrons and is incontact with the first ion conductor (discussed below). The firstelectrode permits (a) conduction of the same ionic species as conductedby the first ion conductor, (b) diffusion of a reduced form of the sameionic species as conducted by the first ion conductor, or both (a) and(b).

In some embodiments, the first electrode is a porous electricallyconductive structure. In some embodiments, the first electrode is aselectively permeable electrically conductive layer. For example, seeU.S. Pat. No. 10,545,461 to Roper et al, which is incorporated byreference herein. In this patent application, “selectively permeable”refers to the transport of metal atoms through the electrode, bydiffusion or conduction. In some embodiments, the first electrode is amixed ion-electron conductor. For example, see U.S. Pat. No. 10,828,618to Roper et al, which is incorporated by reference herein.

The first electrode is preferably a porous electrically conductivelayer. The porous electrically conductive layer is preferably apatterned metal layer directly on one surface of the first ionconductor. The metal layer is preferably thin, such as less than 1micron in thickness, more preferably less than 200 nanometers or lessthan 100 nanometers in thickness. The pattern of the metal layer ispreferably such that metal regions are closely spaced, such as less than100-micron line pitch, more preferably less than 10-micron line pitch,and most preferably less than 2-micron line pitch. The metal layer maybe patterned with photolithography, electron-beam lithography,direct-write lithography, direct-write metal deposition (e.g., ionbeam-induced deposition), interference lithography, etc.

Exemplary electrode materials for the porous electrically conductivelayer include Pt, Mo, W, Ni, Cu, Fe, Al, and combinations thereof. Theporous electrically conductive layer may also entail more than onelayer, such as a Ti adhesion layer and a Pt layer.

The porous electrically conductive layer preferably does not chemicallyinteract with the ionic species conducted by the first ion conductor.For example, the porous electrically conductive layer preferably doesnot form an intermetallic phase and does not chemically react with theionic species other than enabling electrochemical oxidation andreduction. Additionally, the porous electrically conductive layerpreferably does not chemically interact with the first ion conductoritself, other than possible chemical bonding to adhere to the surface ofthe first ion conductor. For example, portions of the porouselectrically conductive layer preferably do not form mobile ions thatare transported to the first ion conductor.

In some embodiments, the first electrode has a high diffusivity for themetal atoms that are sourced. The metal atoms which comprise the atomicvapor have a diffusivity in the first electrode that is preferably atleast about 10⁻¹⁰ cm²/s and more preferably at least about 10⁻⁶ cm²/s,measured at 25° C. or at an operation temperature.

The first electrode is at least a fair electrical conductor. Theelectrical resistivity of the first electrode is preferably less than 10kΩ·cm, more preferably less than 1 kΩ·cm, and most preferably less than1Ω·cm, measured at 25° C.

In some embodiments, the first electrode comprises an intercalationcompound, which is a material capable of being intercalated with atomsof the atomic vapor. In some embodiments, the intercalation compound isgraphite, MoS₂, TaS₂, or a combination thereof, for example. Theintercalation compound may be disposed in a uniform layer that consistsessentially of the intercalation compound and any intercalated atoms.The thickness of the intercalation compound layer is preferably lessthan 100 microns and more preferably less than 10 microns.

In some embodiments, the first electrode comprises particles of anintercalation compound in a matrix. The matrix is preferably a polymerbinder, such as (but not limited to) poly(vinylpyrrolidone)poly(methacrylate), poly(methyl methacrylate), poly(ethyl methacrylate),poly(2-hydroxyethyl methacrylate), fluoroelastomers, cellulose resin, ora combination thereof. The polymer binder preferably has low outgassingat device operating temperature and is compatible with ultra-highvacuum. Matrix additives may be included to increase the electricalconductivity of the first electrode. For example, small conductivecarbon particles may be included (e.g. Super-P® carbon black).

The first electrode may also include a region and/or layer with highelectrical conductivity to minimize sheet resistance of the firstelectrode. For example, the first electrode may consist of two layers: alayer that is substantially graphite and a layer that is a porouselectrically conductive layer, such as a thin platinum mesh. Thislayered configuration may be beneficial to ensure that the electricalpotential, when applied, does not vary considerably (e.g., <0.1 V)across the electrode surface even if an intercalation material hasmediocre electrical conductivity or if an intercalation material is verythin. The highly electrically conductive layer may include Pt, Mo, W, ora combination thereof. The highly electrically conductive layer may alsoentail more than one sub-layer, such as a Ti adhesion sub-layer and a Ptsub-layer. The highly electrically conductive layer preferably does notform an intermetallic phase with, or otherwise chemically react with,the ionic species. The highly electrically conductive layer preferablydoes not chemically interact with the first ion conductor.

In some embodiments, the first electrode is a mixed ion-electronconductor, which means that the first electrode is both an ion conductorand an electron conductor. The mixed ion-electron conductor preferablyhas an electrical sheet resistance less than 10 MΩ/□(10 million ohms persquare), more preferably less than 100 kΩ/□, and most preferably lessthan 1 kΩ/□. The electrical resistivity of the mixed ion-electronconductor is preferably less than 100 kΩ·cm, more preferably less than10 kΩ·cm, and most preferably less than 100 Ω·cm. The ionic conductivityof the mixed ion-electron conductor is preferably at least10⁻¹²Ω⁻¹·cm⁻¹, more preferably at least 10⁻⁹Ω⁻¹·cm⁻¹, and mostpreferably at least 10⁻⁶Ω⁻¹·cm⁻¹. The ionic conductance of the mixedion-electron conductor, through the thickness of the electrode, ispreferably less than 10 kΩ, more preferably less than 1 kΩ, and mostpreferably less than 100Ω.

Exemplary doped mixed ion-electron conductors include, but are notlimited to, Rb_(1−2x)M_(x)AlO₂ (x is from 0 to less than 0.5) whereinM=Pb, Cd, and/or Ca; Rb_(2−2x)Fe_(2−x)M_(x)O₄ (x is from 0 to 1) whereinM=P, V, Nb and/or Ta; Rb_(2−2x)Ga_(2−x)M_(x)O₄ (x is from 0 to 1)wherein M=P, V, Nb and/or Ta; Rb_(2−2x)Al_(2−x)M_(x)O₄ wherein M=P, V,Nb and/or Ta; and Rb_(1−x)Al_(1−x)M_(x)O₂ (x is from 0 to less than 1)wherein M=Si, Ti, and/or Ge.

In some embodiments, the mixed ion-electron conductor material may beselected from alkali pyrophosphates, such as Rb₄P₂O₇. The alkalipyrophosphate is optionally doped with one or more atoms selected fromCa, Sr, Ba, Pb, Y, La, and/or Nd, for example. Exemplary compounds forthe doped alkali pyrophosphates include, but are not limited to,Rb_(4−2x)M_(x)P₂O₇ (x is from 0 to less than 2) wherein M=Ca, Sr, Ba,and/or Pb; and Rb_(3−3x)M_(x)PO₄ (x is from 0 to less than 1) whereinM=Y, La, and/or Nd.

In some embodiments, the mixed ion-electron conductor is a uniform layerthat consists essentially of the mixed ion-electron conductor. Thethickness of the mixed ion-electron conductor material is preferablyabout 500 microns or less, and more preferably about 100 microns orless.

In some embodiments employing a mixed ion-electron conductor, the firstelectrode comprises a region or layer with high electrical conductivityto minimize the electrical sheet resistance of the first electrode. Forexample, the first electrode may include two layers: a layer that is amixed ion-electron conductor and a layer that is a highly electricallyconductive layer (e.g., a thin Pt mesh). The layered configurationallows for the electrical potential, when applied, to not varyconsiderably (e.g., <0.1 V) across the electrode surface even if themixed ion-electron conductor has mediocre electrical conductivity or ifthe mixed ion-electron conductor is very thin. The highly electricallyconductive layer may include Pt, Mo, W, or a combination thereof. Thehighly electrically conductive layer may itself include sub-layers, suchas a Ti adhesion sub-layer and a Pt sub-layer. The highly electricallyconductive layer preferably does not chemically interact with the ionicspecies and preferably does not form an intermetallic phase with theionic species. Also, the highly electrically conductive layer preferablydoes not chemically interact with the first ion conductor. For example,when the highly electrically conductive layer contains Pt, preferablyPt²⁺ or other platinum ions do not become mobile ions within the firstion conductor.

The second electrode is preferably in contact with the first ionconductor. The second electrode is not in electrical contact with thefirst electrode. The second electrode contains at least asecond-electrode first phase that stores and transports neutral atoms.Transport of neutral atoms is preferably via diffusion, and storage ofneutral atoms is preferably via intercalation.

The atomic species contained within the second-electrode first phase arepreferably a reduced form of the same ionic species as in the first ionconductor. Alternatively, or additionally, a different atomic speciesmay be contained within the reservoir. For example, when the device issourcing atoms, Na may be contained within the secondelectrode/reservoir and may be oxidized, while Rb may be reduced at thefirst electrode.

The second-electrode first phase is preferably graphite. Thesecond-electrode first phase may include predominately sp²-bondedcarbon. Examples of sp²-bonded carbon include, but are not limited to,graphite, monolayer graphene, few-layer graphene, graphene flakes, holeygraphene (perforated graphene), carbon nanotubes, fullerenes (e.g., C₆₀,C₇₀, etc.), polyaromatic hydrocarbons (e.g., pentacene, rubrene,hexabenzocoronene, coronene, etc.), chemical-vapor-deposited graphiticcarbon, pyrolyzed carbon-containing molecules or polymers includepyrolyzed parylenes (e.g., pyrolyzed poly(para-xylylene) or analoguesthereof), or combinations of the foregoing.

The second-electrode first phase may alternatively, or additionally,include a metal dichalcogenide. In various embodiments, thesecond-electrode first phase includes a transition metal oxide (e.g.,ZnO), a transition metal sulfide (e.g., MoS₂ or TaS₂), a transitionmetal selenide (e.g., TiSe₂), or a transition metal telluride (e.g.,TiTe₂).

The second-electrode first phase is preferably in the form of particles.It is preferable that the particles have at least one dimension that isrelatively short to reduce the diffusion length for neutral atoms,thereby improving the transport rate. The particles of thesecond-electrode first phase may have a minimum dimension (e.g.,diameter of spheres or rods) of less than 1000 microns, less than 500microns, less than 100 microns, less than 50 microns, less than 10microns, less than 5 microns, less than 1 micron, or less than 500nanometers, for example. In preferred embodiments, the particles of thesecond-electrode first phase have a minimum dimension selected fromabout 100 nanometers to about 20 microns. Particle sizes may be measuredby a variety of techniques, including dynamic light scattering, laserdiffraction, image analysis, or sieve separation, for example.

The second-electrode first phase is preferably a continuous phase or asemi-continuous phase. For example, the second-electrode first phase maybe or include a carbon aerogel, a carbonized polymer, or reticulatedvitreous carbon foam.

The second electrode is preferably electrically conductive. In variousembodiments, the electrical resistivity of the second electrode ispreferably less than 10 kΩ·cm, more preferably less than 1 kΩ·cm, evenmore preferably less than 100Ω·cm, and most preferably less than 10Ω·cm,measured at 25° C.

The thickness of the second electrode may be selected from about 1micron (or less) to about 100 microns (or more). Typically, the secondelectrode is thicker than the first electrode or the third electrode.

In addition to the first phase, the second electrode may contain one ormore other phases to form a composite electrode/reservoir. For example,see U.S. Pat. No. 10,545,461 to Roper et al, which has been incorporatedby reference herein. An additional phase may be an atom-transportingphase that stores and transports neutral atoms. Transport of neutralatoms is preferably via diffusion. At a fixed point in time, neutralatoms may be in the process of being transported into or out of theatom-transporting phase, may be stored at a fixed location within theatom-transporting phase, or may be moving within the atom-transportingphase but not across its phase boundary, and therefore stored withinthat phase. Transport of neutral atoms within the atom-transportingphase and/or across its phase boundaries may occur via various diffusionmechanisms, such as (but not limited to) bulk solid diffusion, porousdiffusion, surface diffusion, grain boundary diffusion, permeation,solubility-diffusion, etc. Storage of neutral atoms is preferably viaintercalation. Storage of neutral atoms also results when the diffusionrate of metal atoms is negligible (e.g., less than 10⁻¹⁰ cm²/s).

In the atom-transporting phase of the second electrode, the selectedmetal atoms may have a diffusion coefficient of at least about 10⁻¹⁰ cm²/s, 10⁻⁹ cm²/s, 10⁻⁸ cm²/s, 10⁻⁷ cm²/s, 10⁻⁶ cm²/s, or 10⁻⁵ cm²/s,measured at the device-operation temperature, such as 25° C., 100° C.,150° C., or 200° C. The metal-atom diffusion in the second electrode asa whole will depend on the bulk diffusivity of the atom-transportingphase, the volume fraction of the atom-transporting phase, and theconnectivity/tortuosity of atom-transporting phase.

The atomic species contained in the atom-transporting phase ispreferably the reduced (neutral charge) form of at least one of theionic species contained in the first ion conductor. Alternatively, oradditionally, the atom-transporting phase may contain an atomic speciesthat is different than the species contained in the first ion conductor.For example, when the device is configured to source atoms, Na may becontained within the atom-transporting phase, Na may be oxidized to Na⁺at the second electrode, Rb⁺ may be reduced to Rb at the firstelectrode, and the first ion conductor may contain both Na⁺ and Rb⁺.

The atom-transporting phase and/or the second-electrode first phasepreferably contain an intercalable compound that is capable of beingintercalated by at least one element in ionic and/or neutral form. Asused herein, an “intercalable compound” (or “intercalatable compound”)is a host material that is capable of forming an intercalation compoundwith guest atoms which comprise the atomic vapor whose density is beingcontrolled. Stated another way, the intercalable compound isintercalative for (capable of intercalating) at least some of the atomsin the atomic vapor. The guest atoms that are intercalated may beneutral atoms, ionic species, or a combination thereof. Typically, theguest atoms are intercalated as neutral atoms.

In some embodiments, the host material actually contains the guestspecies, resulting in a material which may be referred to as an“intercalation compound.” It is noted that for the purposes of thispatent application, any reference to intercalable compound may bereplaced by intercalation compound, and vice-versa, since anintercalable compound must be capable of intercalating a guest speciesbut may or may not actually contain the intercalated guest species.

“Intercalation” herein is not limited to the reversible inclusion orinsertion of an atom, ion, or molecule sandwiched between layers presentin a compound, which shall be referred to herein as “layerintercalation.” Intercalation also includes absorption of neutral atomsor ionic species into a bulk phase of the compound, whether that phaseis amorphous or crystalline; adsorption of neutral atoms or ionicspecies onto an outer surface or an internal surface (e.g., a phaseboundary) present in the compound; and reversible chemical bondingbetween the neutral atoms or ionic species, and the compound.

Some embodiments of the invention utilize layer intercalation, in whicha guest species such as K expands the van der Waals gap between sheetsof a layered compound such as graphite. This layer expansion requiresenergy. Without being limited by theory, the energy may be supplied byelectrical current to initiate charge transfer between the guest (e.g.,K) and the host solid (e.g., graphite). In this example, potassiumgraphite compounds such as KC₈ and KC₂₄ may be formed. These compoundsare reversible, so that when the electrical current is adjusted, thepotassium graphite compounds may give up the intercalated atoms (K).Those previously intercalated atoms may be released into the vapor phaseor into the first ion conductor, for example. Electrical energy may besupplied to cause a chemical potential change at the interface with theintercalable compound, which then causes layer expansion.

In some embodiments, the intercalable compound is a carbonaceousmaterial, such as a material selected from the group consisting ofgraphite, graphite oxide, graphene, graphene oxide, holey graphene,graphene platelets, carbon nanotubes, fullerenes, activated carbon,coke, pitch coke, petroleum coke, carbon black, amorphous carbon, glassycarbon, pyrolyzed carbon-containing molecules, pyrolyzed parylene,polyaromatic hydrocarbons, and combinations thereof.

The intercalable carbonaceous material may be at least 50 wt % carbon,preferably at least 75 wt % carbon, more preferably at least 90 wt %carbon, most preferably at least 95 wt % carbon. In some embodiments,the carbonaceous material is essentially pure carbon, except forimpurities. The carbonaceous material may include mesoporous carbon,microporous carbon, nanoporous carbon, or a combination thereof.

The intercalable carbonaceous material may be a form of predominatelysp² bonded carbon. Examples of sp² bonded carbon include, but are notlimited to, graphite, graphene, carbon nanotubes, carbon fibers,fullerenes (e.g. C₆₀ or C₇₀), pyrolyzed carbon-containing molecules orpolymers (such as pyrolyzed parylene, e.g. parylene-N, parylene-C, orparylene-AF-4), and large polyaromatic hydrocarbons (e.g. pentacene,rubrene, hexabenzocoronene, or coronene). In the case of graphene (whichis essentially a single layer of graphite), the graphene may bemonolayer graphene or multiple layers of graphene. Graphene flakes (afew layers of graphene) may be utilized. Certain embodiments utilizemonolayer holey graphene, multiple layers of holey graphene, or grapheneplatelets.

In certain embodiments, the carbonaceous material comprises graphite.Graphite consists of planes of carbon sheets. Metal atoms, especiallyalkali atoms, readily intercalate between these carbon sheets, leadingto a high diffusivity for those atoms. Graphite electrodes enable fastmetal transport at low voltages and low power consumption per atomremoved. Graphite not only transports atoms via intercalation, but alsois electrically conductive due to the electron delocalization within thecarbon layers. Valence electrons in the carbon are free to move, therebyconducting electricity through the graphite.

The graphite may be natural graphite (e.g., mined graphite) or syntheticgraphite produced from various techniques. For example, graphite may beobtained from chemical-vapor-deposited graphitic carbon, carbide-derivedgraphite, recycled graphite, waste from graphene manufacture, and so on.Crystalline flake graphite occurs as isolated, flat, plate-likeparticles with hexagonal edges if unbroken; when broken the edges can beirregular or angular. Amorphous graphite is very fine flake graphite.Lump graphite occurs in fissure veins or fractures and appears asmassive platy intergrowths of fibrous or acicular crystallineaggregates. Highly oriented pyrolytic graphite is graphite with anangular spread between the graphite sheets of less than 1°.

The graphite may be crystalline, amorphous, or a combination thereof.The graphite crystallinity may range from about 10% to about 90%, forexample. A mixture of crystalline and amorphous graphite may bebeneficial for intercalation not only between crystal layers but alsobetween crystalline and amorphous regions of the graphite. With too muchcrystallinity, the diffusivity becomes highly anisotropic. If highlycrystalline (i.e. highly anisotropic) graphite is oriented with thelow-diffusivity axis normal to the surface of the device (which is atypical orientation), reduced alkali flux, and thus reduced performance,would result.

In some embodiments, the intercalable compound of the atom-transportingphase is a transition-metal oxide, a transition-metal dichalcogenide, ora combination thereof. The intercalable compound may also be a mixtureof a carbonaceous material and a transition-metal oxide, or a mixture ofa carbonaceous material and a transition-metal dichalcogenide, or amixture of all of these materials. Specifically, the intercalablecompound may be a metal dichalcogenide selected from MoS₂, TaS₂, TiTe₂,or any other transition metal dioxide, disulfide, diselenide, orditelluride.

The second electrode is preferably encapsulated by the first ionconductor and one or more reservoir walls. The encapsulation may be asingle encapsulate (e.g., UHV epoxy) or a bonded substrate employing UHVepoxy or thermocompression-bonded silicon, borosilicate glass, oralumina die, for example.

The first ion conductor preferably has high ionic conductivity for aselected ionic species. The ionic conductivity is preferably at least10−7 S/cm, and more preferably at least 10⁻⁵ S/cm, measured at 25° C. orat a device operating temperature. The ionic species may be an ionizedform of an atom of interest in atomic physics and atomic measurementinstruments. In various embodiments, the ionic species is selected fromthe group consisting of Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Sr⁺, Sr²⁺, Ca⁺, Ca²⁺,Ba⁺, Yb²⁺, Yb³⁺, Hg⁺, Hg^(2°), and combinations thereof (i.e., multipleions may be present in the device).

The first ion conductor preferably includes a solid electrolyte. Forexample, the first ion conductor may be a large fraction (>50% byweight) β-alumina, β″-alumina, or a combination of β-alumina andβ″-alumina. β-alumina and β″-alumina are good conductors of their mobileions yet allow negligible non-ionic (i.e., electronic) conductivity.β″-alumina is a hard polycrystalline or monocrystalline ceramicmaterial. β-alumina and/or β″-alumina are also referred to herein as“beta-alumina.” When prepared as a solid electrolyte, beta-alumina iscomplexed with a mobile ion, such as Na⁺, K⁺, Li⁺, Rb⁺, Cs⁺, Sr²⁺, orCa²⁺, in which case the material becomes sodium-beta-alumina,potassium-beta-alumina, lithium-beta-alumina, rubidium-beta-alumina,cesium-beta-alumina, strontium-beta-alumina, or calcium-beta-alumina,respectively.

Other possible solid electrolyte materials for the first ion conductorinclude yttria-stabilized zirconia, NASICON, LISICON, KSICON,alkali-ion-exchanged versions thereof, and combinations of any of theforegoing. In these or other embodiments, chalcogenide glasses may beused as solid electrolyte materials for the first ion conductor.Exemplary chalcogenide glasses include, but are not limited to,RbI—GeSe₂—Ga₂Ge₃ and CsI—GeSe₂—Ga₂Ge₃.

The atomic-beam source device may include an atom reservoir that isdistinct from the second electrode/reservoir. This additional atomreservoir is preferably in contact with the second electrode. The atomreservoir may be comprised, in part or in whole, by graphite orgraphitic carbon. The graphite or graphitic carbon provides electricalconductivity and also a means of storing atoms, such as in a graphiteintercalation compound.

The atom reservoir may contain metal in the vapor phase and possibly insolid and/or liquid phases as well. The atomic species contained withinthe atom reservoir is preferably the reduced form of the same ionicspecies as in the first ion conductor. Alternatively, a different atomicspecies may be contained within the atom reservoir.

The atom reservoir and/or the second electrode may be designed toaccommodate any mechanical strain from a changing reservoir volume dueto the loss or introduction of atoms. For instance, a gap may besituated between an intercalation compound and the reservoir walls topermit expansion of the intercalation compound without straining thereservoir walls. The reservoir walls may be designed to elasticallyand/or plastically deform. This configuration may be accomplishedthrough material selection (e.g. metals, polymers, or a combinationthereof). Alternatively, or additionally, this configuration may beaccomplished through reservoir design (e.g. a bellows).

The atom reservoir and/or the second electrode has walls that arepreferably impermeable to the atomic species contained inside thereservoir. The walls are preferably thin films and supported by asubstrate (e.g. glass, Si, alumina, etc.). The side(s) of the reservoirwalls that face the interior of the reservoir preferably do notchemically interact with the ionic species. For example, the reservoirwalls do not form an intermetallic phase with the ionic species and donot chemically react with the ionic species. Exemplary reservoir wallmaterials include Pt, Mo, W, or a combination thereof, for the wallsthat face the interior of the reservoir. When there are side(s) of thereservoir walls that touch the first ion conductor, the reservoir wallspreferably do not chemically interact with the first ion conductor,other than chemical bonding to adhere to the first ion conductor.Exemplary reservoir wall materials include Pt, Mo, W, or a combinationthereof, for the walls (if any) that touch the first ion conductor.

Multiple ion conductors, each with their own electrodes, may be presentin a single device. Multiple first electrodes may or may not beelectrically connected through electrical leads or electrical traces.Likewise, multiple second electrodes may or may not be electricallyconnected through electrical leads or electrical traces.

Multiple sets of first electrodes, ion conductors, and second electrodesmay generally be present. In some embodiments, two or more first (front)electrodes are employed. In these or other embodiments, two or moresecond (back) electrodes are employed. In any of these embodiments, orother embodiments, two or more ion conductors are employed.

Each electrode is typically connected to an electrical lead fabricatedfrom an electrically conductive material. A lead is an electricalconnection consisting of a length of wire, metal pad, metal trace, orother electrically conductive structure. Leads are used to transferpower and may also provide physical support and potentially provide aheat sink. In some embodiments, a device is provided without such leads,which may be added at a later time, before use.

There are many options for the electrical connections to the first andsecond electrodes of the atomic-beam source device. The electricalconnections may be connected to bond pads for connection to an externalcircuit. The electrical connections may include through-wafer vias,patterned electrically conductive thin films, doped regions ofsemiconductors, wire bonds, or a combination thereof. Patterned thinfilms may be parallel with the first electrode, such as when the firstelectrode is substantially flat. Parts of patterned thin films may be atan angle with the first electrode. In some embodiments, the electrodeconnections travel out of the plane of the electrode to which it isconnected.

The atomic-beam source device may be contained within an oven. Thepurpose of the oven may be to control the temperature of the device at atemperature above the ambient temperature, for example. In principle,the atomic-beam source device may be contained within any sort oftemperature-controlled system, for heating or cooling the device.

The atomic-beam source device may be operated at a wide range oftemperatures and pressures. In various embodiments, the atomic-beamsource device may be operated at a temperature from about −200° C. toabout 500° C., preferably from about −50° C. to about 250° C., and morepreferably from about 10° C. to about 200° C. After atoms are emittedfrom the atomic-beam source device, those atoms may be cooled toultra-low temperatures (e.g., 10⁻⁷ K to 10⁻³ K) as needed for someapplications or measurements. In various embodiments, the atomic-beamsource device may be operated at a pressure from about 7600 torr (10atm) to about 10⁻¹⁴ torr, preferably from about 10⁻³ to about 10⁻¹³torr, and more preferably from about 10⁻⁷ torr to about 10⁻¹² torr.

The atomic-beam source device may include an integrated heater. Theintegrated heater may be a resistive heater, such as a thin wire or apatterned thin metal trace (e.g. Pt or nickel-chromium alloy). Theintegrated heater may also be a radiative heater or a thermoelectricheater, for example. The integrated heater preferably includes atemperature sensor, such as a thermocouple or a resistance temperaturedetector (e.g., Pt). Preferably, the heater is in good thermalcommunication with the region of the first ion conductor that is nearthe first electrode.

In some embodiments, the atomic-beam source device is a chip-scaledevice that is mounted or integrated on a microelectromechanical systems(MEMS) heater stage to minimize heater power.

When an integrated heater is included in the device, the heater mayfurther comprise one or more thermal isolation structures. A thermalisolation structure minimizes heat transfer from the heated region ofthe device to the colder, ambient environment. A thermal isolationstructure is configured to minimize heat loss out of the heated regioninto a cold region, by functioning as insulation to retain heat withinthe heated region. The thermal isolation structure preferably has a highvalue of thermal resistance, as further explained below.

A thermal isolation structure may be made of the same material and layeras the atom reservoir walls, in some embodiments. In these or otherembodiments, a thermal isolation structure may be made of the samematerial and layer as the first ion conductor. The thermal isolationstructure is preferably polymer, ceramic, or glass, although metal maybe utilized as well, or a combination of the foregoing.

In some embodiments, the thermal isolation structure is fabricated froma material selected from the group consisting of β-alumina (e.g.,Rb-β-alumina, Na-β-alumina, or Sr-β-alumina), β″-alumina (e.g.,Rb-β″-alumina, Na-β″-alumina, or Sr-β″-alumina), α-alumina, silica,fused silica, quartz, borosilicate glass, silicon, silicon nitride,silicon carbide, and combinations thereof.

The thermal isolation structure may be designed to accommodate materialswith any thermal conductivity. High-thermal-conductivity materials willbenefit from long, high-aspect ratio connections, whilelower-thermal-conductivity materials may utilize shorter, stubbierconnections.

An important design parameter for the thermal isolation structure (whenpresent) is the thermal resistance. The thermal resistance is thetemperature difference across the thermal isolation structure when aunit of heat energy flows through it in unit time; or equivalently, thetemperature difference, at steady state, between two defined surfaces ofthe thermal isolation structure that induces a unit heat flow rate.Because the desire is for a low heat flow rate, a high temperaturedifference is desired, i.e., a high value of thermal resistance. Thethermal resistance of a thermal isolation structure is preferably atleast 100 K/W, more preferably at least 1,000 K/W, and most preferablyat least 10,000 K/W.

A thermal isolation structure may also be configured to impartmechanical strain relief, thereby preventing mechanical damage due tothermal strains that build up when the first ion conductor is heated toa higher temperature than the base substrate. In some embodiments, athermal isolation structure is mechanically connected to a basesubstrate, for example through a frame. Preferably, the thermalisolation structure is designed to reduce thermal stress or residualstress by at least 2×, preferably at least 10×, and more preferably atleast 100× from one side of the thermal isolation structure to the otherside. The thermal or residual stress reduction is not an inherentmaterial property, but is a function of the geometric design of thethermal isolation structure and its material properties.

In some embodiments, a thermal isolation structure is a suspension beam.Typically, a plurality of suspension beams will be present to connectthe heated region to the cold region. The heated region only contactsthe cold region through the suspension beams. The suspension beams maybe straight beams, folded beams, tortuous beams, circular beams, and soon. The suspension beams may be made in any one (or more) layers in aplanar process, such as surface or bulk micromachining. The rest of theheated region may be surrounded by vacuum or a vapor phase (e.g.,containing an inert gas), either of which has a high thermal resistanceto the cold region. As an alternative, the vapor/vacuum region mayinclude a thermal insulator material, such as an aerogel.

In some embodiments, a thermal isolation structure has a thin metal filmpatterned on it for electrical interconnections. In some preferredembodiments, a resistive heater and a temperature sensor are patternedon (in contact with) the same layer as at least one thermal isolationstructure. Preferably, electrical connections to the heater and thetemperature sensor are also patterned on one or more thermal isolationstructures. Optionally, part or all of the heater may be patterned on athermal isolation structure or on multiple thermal isolation structures.In some embodiments, a thin film resistive heater is patterned on one ormore sides of the same layer as a thermal isolation structure. In caseswhere the first ion conductor is separate from the thermal isolationstructure, the heater may be patterned on the same side or the oppositeside of the thermal isolation structure compared to the position of thefirst ion conductor. In cases where the first ion conductor is the sameas a thermal isolation structure, or a layer thereof, the heater may bepatterned on either side of the first ion conductor (i.e. on thefirst-electrode side and/or on the second-electrode side). See commonlyowned U.S. patent application Ser. No. 16/573,684, filed on Sep. 17,2019, which is hereby incorporated by reference herein.

The integration of the heater and thermal isolation structures withinthe system enables low system power input. The system power input forcontrolling vapor density of metal atoms is preferably less than about500 mW, more preferably less than about 200 mW, and most preferably lessthan about 100 mW. In various embodiments, the system power input forsourcing and/or sinking metal atoms is about 1000, 500, 400, 300, 200,100, 50, 25, or 10 mW.

In some embodiments in which high vapor density is desirable, thedensity of metal atoms may be at least 10⁹ atoms per cm³, preferably atleast 10¹⁰ per cm³, and more preferably at least 10¹¹ per cm³. In someembodiments in which low vapor density is desirable, the density ofmetal atoms may be below 10⁸ atoms per cm³, preferably below 10⁷ atomsper cm³. In various embodiments, the density of metal atoms if about, atleast about, or at most about 10⁶ atoms per cm³, 10⁷ atoms per cm³, 10⁸atoms per cm³, 10⁹ atoms per cm³, 10¹⁰ atoms per cm³, 10¹¹ atoms percm³, or 10¹² atoms per cm³.

The atomic-beam source device may be fabricated on a wide variety oflength scales. The length scale may be characterized by the square rootof the first electrode area. This length scale may vary from 10 m to 1micron, with 1 m to 10 mm being typical for macroscale atomic timing andnavigation systems, and 30 mm to 10 microns being typical for chip-scaleatomic timing and navigation systems.

Chip-scale devices are preferably constructed using microfabricationtechniques, including some or all of lithography, evaporation,shadow-masking, evaporation, sputtering, wafer bonding, die bonding,anodic bonding, glass frit bonding, metal-metal bonding, and etching.

This disclosure hereby incorporates by reference herein the followingpatents for teaching solid-state electrochemical atom sources that areused in some embodiments, as atom sources and/or atom sinks: U.S. Pat.No. 9,763,314, issued Sep. 12, 2017; U.S. Pat. No. 9,837,177, issuedDec. 5, 2017; U.S. Pat. No. 10,056,913, issued Aug. 21, 2018; U.S. Pat.No. 10,545,461, issued Jan. 28, 2020; U.S. Pat. No. 10,775,748, issuedSep. 15, 2020; U.S. Pat. No. 10,828,618, issued Nov. 10, 2020; and U.S.Pat. No. 11,101,809, issued Aug. 24, 2021. All publications, patents,and patent applications cited in this specification are hereinincorporated by reference in their entirety as if each publication,patent, or patent application were specifically and individually putforth herein.

In this detailed description, reference has been made to multipleembodiments and to the accompanying drawings in which are shown by wayof illustration specific exemplary embodiments of the invention. Theseembodiments are described in sufficient detail to enable those skilledin the art to practice the invention, and it is to be understood thatmodifications to the various disclosed embodiments may be made by askilled artisan.

Where methods and steps described above indicate certain eventsoccurring in certain order, those of ordinary skill in the art willrecognize that the ordering of certain steps may be modified and thatsuch modifications are in accordance with the variations of theinvention. Additionally, certain steps may be performed concurrently ina parallel process when possible, as well as performed sequentially.

The embodiments, variations, and figures described above should providean indication of the utility and versatility of the present invention.Other embodiments that do not provide all of the features and advantagesset forth herein may also be utilized, without departing from the spiritand scope of the present invention. Such modifications and variationsare considered to be within the scope of the invention defined by theclaims.

What is claimed is:
 1. An interferometric frequency-reference apparatus,said apparatus comprising: a vacuum chamber; an atom source configuredto supply neutral atoms; a collimator configured to form a collimatedbeam of said neutral atoms; one or more probe lasers; and a readoutlaser configured to determine a ground-state population of said neutralatoms, wherein said atom source and said collimator are disposed withinsaid vacuum chamber.
 2. The interferometric frequency-referenceapparatus of claim 1, wherein said atom source is a solid-stateelectrochemical atom source.
 3. The interferometric frequency-referenceapparatus of claim 1, wherein said collimator is a linear collimator. 4.The interferometric frequency-reference apparatus of claim 3, whereinsaid linear collimator is selected from the group consisting of a linearquadrupole trap, a Penning trap, and a mass filter.
 5. Theinterferometric frequency-reference apparatus of claim 1, wherein saidcollimator is a non-linear collimator.
 6. The interferometricfrequency-reference apparatus of claim 5, wherein said non-linearcollimator is in a recirculating configuration.
 7. The interferometricfrequency-reference apparatus of claim 1, wherein said one or more probelasers are configured for Ramsey spectroscopy on said neutral atoms. 8.The interferometric frequency-reference apparatus of claim 1, whereinsaid one or more probe lasers is two or more probe lasers.
 9. Theinterferometric frequency-reference apparatus of claim 1, wherein saidone or more probe lasers are configured to probe quadrupole or bothdipole and quadrupole transitions of said neutral atoms.
 10. Theinterferometric frequency-reference apparatus of claim 1, wherein saidinterferometric frequency-reference apparatus further comprises acooling laser.
 11. The interferometric frequency-reference apparatus ofclaim 1, wherein said readout laser is further configured for cooling.12. The interferometric frequency-reference apparatus of claim 1,wherein said interferometric frequency-reference apparatus furthercomprises an imaging system configured to focus fluorescence from saidneutral atoms.
 13. The interferometric frequency-reference apparatus ofclaim 1, wherein said interferometric frequency-reference apparatusprovides an optical frequency reference.
 14. The interferometricfrequency-reference apparatus of claim 1, wherein said interferometricfrequency-reference apparatus provides a microwave frequency reference.15. A method of creating a stable frequency reference, said methodcomprising: (a) creating an atomic vapor of neutral atoms; (b)collimating said neutral atoms in a collimator, to form a collimatedbeam of said neutral atoms; (c) optionally, illuminating some of saidneutral atoms with a cooling laser; (d) illuminating at least some ofsaid neutral atoms with a first probe laser at a first-probe-laserfrequency; (e) illuminating at least some of said neutral atoms with asecond probe laser at a second-probe-laser frequency; (f) adjusting saidfirst-probe-laser frequency and said second-probe-laser frequency usingRamsey spectroscopy to an S D transition of at least some of saidneutral atoms; and (g) illuminating at least some of said neutral atomswith a readout laser to determine a ground-state population of saidneutral atoms.
 16. The method of claim 15, wherein said neutral atomsare obtained from a solid-state electrochemical atom source.
 17. Themethod of claim 15, wherein step (c) is conducted to cool said neutralatoms in preparation for said Ramsey spectroscopy.
 18. The method ofclaim 15, wherein said collimator is a linear collimator.
 19. The methodof claim 18, wherein said linear collimator is selected from the groupconsisting of a linear quadrupole trap, a Penning trap, and a massfilter.
 20. The method of claim 15, wherein said collimator is anon-linear collimator.
 21. The method of claim 20, wherein saidnon-linear collimator is in a recirculating configuration.
 22. Themethod of claim 15, wherein said method further comprises illuminatingat least some of said neutral atoms with a third probe laser.
 23. Themethod of claim 22, wherein said method further comprises illuminatingat least some of said neutral atoms with a fourth probe laser after saidilluminating at least some of said neutral atoms with said third probelaser.
 24. The method of claim 15, wherein said method is continuous.25. The method of claim 15, wherein said stable frequency reference isan optical frequency reference.
 26. The method of claim 15, wherein saidstable frequency reference is a microwave frequency reference.